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Stochastic  Control  in  Eye  Movement  Tracking 


By 

r  -* 

Shean  Wang  i 
t-   •+ 


RESEARCH  PROJECT 

Submitted  in  partial  satisfaction  of  the  requirements  for  the  degree  of 

MASTER  OF  SCIENCE 

in 
Electrical  Engineering  and  Computer  Sciences 

in  the 
GRADUATE  DIVISION 

of  the 
UNIVERSITY  OF  CALIFORNIA,  BERKELEY 


Approved: 


Lawrence   Stark,    Research  Adf/i  so  r  Edwin   R.    Lewis,    Research   Advisor 


T7 


INTRODUCTI^II 1 

sxp3T.i::.::Trj:         JIIOD 3 

033EHVA-TIOU  ?^Ci:  OJHZ  EXP2S1MEIITAL  RZ3UL23. 6 

DISCUSSION 9 

POSSIBLE  ?U2URE  Din2CO?lCi; 24 

SUI'2>iASY 26 

RZFSREKCI 28 

PIGUHSS 29-72 


range  of  fr-jcuer.cy ,  the  eye  can  even  anticipate  the 
target.  This  leads  numerous  models  of  a  predictor  for 
the  eye  movement  systen.  Consequently,  an  effort  is  made 
to  compare  the  experimental  results  of  this  report  with 
those  of  existing  proposed  models. 
II.  The  pursuit  and  saccadic  movements  of  eyes. 

Many  established  experiments  have  shown  that  the  afferent 
signals  are  continuous  but  the  efferent  signals  are 
either  continuous  or  discrete  or  both.  Thus  the 
respective  eye  movement  can  be  pursuit,  saccadic,  or  both 
pursuit  and  saccadic.  Therefore,  questions  are  raised 
about  the  discrete  nature  of  eye  movements.  Where  does 
the  discrete  nature  come  from?  How  does  it  work?  As  of 
now,  there  is  no  physiological  explanation.  However,  from 
the  engineering  point  of  view,  there  can  be  numerous 
possibilities.  The  most  satisfactory  model  is  a 
stochastic  sample-data  control  system  with  a  uniformly 
distributed  inter-sampling  time.  This  system  v/ill  be 
reviewed  in  this  reoort. 


.  -i.  .  :--•-.  _  ;-. 

The  experimental  procedure  for  the  measurement  of  horizontal 
eye  movements  has  been  well  established  and  therefore  only  a 
brief  description  v.-ill  be  presented  here. 

In  a  dark  room,  the  subject  v;as  asked  to  fixate  on  a  light 
spot  which,  is  controlled  by  a  target  notion  generator.  A 
small  beam  of  infra-rad  light  was  directed  to  the  left  eye 
ball,  and  its  reflection  was  collected  by  a  pair  of 
photocells  aimed  at  the  iris-scleral  border  as  shown  in 
Figure  3a.  2ye  positions  could  be  detected  by  the  difference 
in  output  of  these  two  photocells.  Then  an  operational 
amplifier  was  used  to  amplify  the  difference  and  send  it  to 
a  Sanborn  recorder.  In  order  to  minimize  the  interference 
introduced  by  motion,  the  subject  leaned  his  forehead 
against  =i  fir™  b?.r  ?.nd  bit  on  a  piece  of  dinLal  iia^ression 
wax  as  shown  in  Figure  3t>. 

Experimental  data  were  collected  from  three  subjects.  Three 
different  kinds  of  stimuli  were  presented:  regular  square 
wave,  irregular  square  wave  (or  staircase  wave),  and  ramp 
input.  The  latency  of  response  to  each  stimulus  could  be 
defined  in  three  different  ways  as  shown  in  Figure  4a,  4b, 
and  4-c.  However,  in  Figure  4-c,  it  was  very  hard  to  decide  to 
which  particular  input  the  eye  did  respond.  The  time  required 
for  eye  to  respond  upon  a  stimulus  (reaction  time)  was  about 
150  msec,  therefore,  the  tine  larger  than  but  closest  to 
150  msec  was  choosen. 

For  each  experimental  run,  a  histogram  of  latency  of 
response  was  generated.  The  binwidth  was  25  msec,  and  the 
middle  point  of  each  bin  was  used  as  the  latency  within  its 


+  12  msec  range  (see  Figure  5  to  Figure  11).  The  average 
and  standard,  deviation  of  latency  were  computed  by  IBM  6A-00 
for  each  experimental  run  of  both  square  wave  and  staircase 
wave  stimuli.  A  set  of  experimental  data  v;as  collected  from 
the  same  subject  with  the  sane  stimulus  by  changing  the 
frequency  alone.  The  frequencies  used  are  listed  in  Table  1 
(see  next  page).  For  each  set  of  square  wave  and  staircase 
wave  experimental  runs,  the  inedian(H),  average(Av),  mode(Hd), 
and  standard  deviation(s)  of  latency  were  ploted  vs. 
frequency  as  shown  in  Figure  5  to  Figure  10.  In  the  ramp 
input  case,  only  median  vs.  frequency  was  ploted. 


Set  I.  Regular  square  v/ave  input! 


1. 

2. 

3. 
4. 

5. 
6. 

7. 

8. 

9. 
10. 

0.1  Hz. 
0.3  Hz. 
0.5  Hz. 
0.9  Hz. 
1.1  Hz. 
1.3  Hz. 
1.5  Hz. 
1.7  Hz. 
1.9  Hz. 
2.3  Hz. 

Set  II_.  Irregular  square 

v/ave  inputs: 

1. 

0 

.150  Hz, 

0 

.235 

Hz, 

0 

.488 

Hz 

2. 

0 

.255  Hz, 

0 

.488 

Hz, 

0 

.785 

Hz 

3. 

0 

.488  Hz, 

0 

.785 

Hz, 

1 

.230 

Hz 

4. 

0 

.785  Hz, 

1 

.230 

Hz, 

1 

.480 

Hz 

5. 

1 

.230  Hz, 

1 

.480 

Hz, 

1 

.710 

Hz 

6. 

1 

.480  Hz, 

1 

.710 

Hz, 

1 

.950 

Hz 

7. 

1 

.710  Hz, 

1 

.950 

Hz, 

2 

.210 

Hz 

8. 

1 

.950  Hz, 

2 

.210 

Hz, 

2 

.450 

Hz 

9. 

2 

.210  Hz, 

2 

.450 

Kz, 

2 

.730 

Hz 

10. 

2 

.450  Hz, 

2 

.730 

Hz, 

3 

.010 

Hz 

Set  III.  Samp 

inputs: 

1. 

2 

°/sec. 

2. 

1 

°/sec. 

3. 

0 

.7°/sec. 

4. 

0 

•  o?'j  /sec. 

5. 

0 

,5°/sec. 

6. 

0.33°/sec. 

7. 

O.l33°/sec. 

8. 

1 

•6°/sec. 

Table  1 . 


'T  ;1 

-lj_. 


(A)  Regular  square  v;ave  inputs: 

The  results  from  subject  C  (Figure  5)  and  subject  W  ( 
Figure  7)  give  similar  conclusior.  for  the  values  of  the 
median,  the  average,  and  the  mode  of  the  latency 
distribution  curve.  They  shov;  that  these  three  values  are 
all  frequency  dependent.  But  at  the  meantime,  subject  C 
and  subject  S  shov/  a  similarity  in  the  curve  of  the 
standard  deviation  of  latency  distribution  vs.  frequency. 
That  is,  the  standard  deviation  of  the  latency 
distribution  is  also  frequency  dependent. 

For  the  latency  distribution  curve, 
Let       M  =  median 
Av  =  average 
lid  =  mode 

s  =  standard  deviation 
then  the  above  similarities  can  be  summarized  as  follows: 

(1)  0^  frequency  <O.  5  Hz. 

a.  M,  Av,  Hd  are  all  decreasing  as  frequency 
increasing. 

b.  s  is  increasing  as  frequency  increasing. 

(2)  0.5  Hz.^  frequency  <  1.5  Hz. 

a.  M,  Av,  and  Md  are  within  +  25  msec  range. 

b.  s  is  decreasing  as  frequency  increasing. 
(5)  frequency>1.5  Hz. 

M,  Av,  Ivd,  and  s  are  increasing  as  frequency 
increasing. 

Therefore  the  distribution  of  latency  is  shifted  as 
frequency  is  changed.  The  distribution  starts  at  the  large 
time  l-.g  region,  then  shifts  to  the  tine  lead  region.  As 


frequency  continue  3  J;o  increase,  it  shifts  back  tov:ards 
the  time  region.  Subject  3  (Figure  8)  yields  a  set  of 
different  results  for  ~~:ic.n,  average,  and  node.  These 
three  values  are  all  betv;een  100  nsec  and  175  msec.  The 
distribution  curves  do  not  have  any  obvious  shift  as 
frequency  changed. 


The  standard  deviation  curve  from  subject  W  shows  that  the 
value  varies  betv;een  +_  35  msec  to  +  88  "sec,  and  it  is 
frequency  independent. 

Despite  the  differences  among  the  above  discussed  three 
subjects,  they  do  have  seme  similarities.  When  frequency 
was  increased,  the  number  of  abnormal  responses  of  all 
three  subjects  would  increase,  and  their  distribution 
curves  all  were  normal  form. 


(  r-»  +-  Q  n  -r"»/->or*^N   T.TOTr^  i    f  TJ*-?  i~n*-*\s\   Q   4-  ••» 
V^-;  v—_-^  ^  •->._•  ~   ..^Vt-y   x-  J-j-j*—  ^   %_;   ow 

Figure  10)  : 

The  median,  average,  mode,  and  standard  deviation  of  the 
latency  distribution  are  not  all  frequency  dependent.  The 
values  of  median,  average,  and  mode  varied  within  the  range 
of  150  msec  to  250  msec.  But  the  shape  of  the  latency 
distribution  curve  seems  to  be  frequency  dependent.  As 
frequency  increases  the  distribution  curve  tends  to  change 
its  shape  from  a  nor~al  distribution  to  a  square  form 
distribution.  This  change  can  be  observed  by  comparing 
Figure  Sa  to  8c  Figure  9a  to  9c,  and  Figure  10a  to  10c. 

(C)  Ramp  inputs  (Figure  11): 

(1)  The  speed  of  target  0.33°/sec: 
Latency  decreased  as  speed  increased. 

(2)  0.53°/sec  the  speed  of  target  0.83°/sec: 

As  speed  increased,  the  latency  of  response  to  the 
continuous  portion  increased  (Figure  11),  and  the 


8 


latency  of  response  to  the  discontinuous  portion 
decreased  (Figure  11). 
O)  Tiie  speed  of  the  target  O.G5°/3ec: 

Latency  of  response  decreased  as  speed  decreased. 
The  latency  of  response  to  the  discontinuous  portion 
is  much  less  than  the  latency  of  response  to  the 
continuous  portion  as  shown  in  Figure  11d. 


In  this  report,  the  discussion  was  divided  as  tv/o  parts:  one 
emphasises  the  pattern  recognition  associated  with  the  eye 
movement,  the  other  one  concentrates  on  the  discrete  nature 
of  eye  movement.   In  either  case,  different  models  were 
discussed.  Comparison  was  made  between  models  or  between 
those  models  and  my  experimental  results. 

There  were  three  models  discussed  in  the  pattern  recognition 
phenomenon,  namely,  Dallos  and  Jones'  model,  Susie's  model 
Cyr  and  Fender's  model.   In  the  discrete  phenomenon, 
Forster's  model  was  reviewed,  and  Latour's  experimental 
results  were  mentioned. 

(A)  Pattern  Recognition 

(1)  Dallos  and  Jones'  model: 

From  the  above  presentation,  it  is  obvious  that  the 
distribution  of  latency  is  very  much  dependent  upon  both 
the  wave  form  and  the  frequency  of  the  stimulus.   In 
fact,  this  is  the  property  that  led  Dallos  and  Jones'" 
to  theorize  about  the  "acquisition  of  learning".  From 
their  theor;/,  a  model  is  proposed.  Three  properties 
of  this  model  are  worth  discussing,  namely,  learning 
speed,  prediction,  rnd  detection. 

(a)  Learning  Speed 

By  examining  the  first  few  cycles  of  tracking  responses 
to  sinusoidal  and  square  wave  inputs  (Figure  12),  Dallos 
and  Jones  believed  that  the  rate  of  learning  was 
considerably  greater  for  continuous  than  for  discontinuous 
input  with  the  same  frequency.   But  from  my  experimental 


observation  (see  previous  section  and  Figure  lid),  the 
response  of  the  ramp  tracking  shov/ed  that  it  is  not  so. 
When  "both  continuous  and  discontinuous  changes  were  presented 
in  a  repetitive  manner,  namely  the  ramp  stimulus,  the  rate 
of  learning  in  the  discontinuous  portion  was  faster  than  that 
of  continuous  portion  (Figure  11d),  thus  contradicted  their 
conclusion.   Therefore,  the  correlation,  if  any,  between  the 
rate  of  learning  and  the  continuity  of  stimuli  remains  still 
a  question. 

(b)  Predictor 

For  each  input  stimulus,  an  output  Bode  plot  v;as  ploted. 
Then  the  corresponding  closed-loop  transfer  function  was 
obtained  by  curve  fitting.  Basing  on  the  assumption  of 
linearity  and  unit  feedback,  the  corresponding  open-loop 
transfer  function  for  each  stimulus  can  be  computed  froa 
its  closed-loop  trancf  c-r  function. 

Let  GI)(ov/)=  closed-loop  transfer  function  for  sinusoidal 

input . 
G(jw)  =  closed-loop  transfer  function  for  random 

input . 
gr>(dw)=  open-loop  transfer  function  for  sinusoidal 

input . 
g(jv;)  =  open-loop  transfer  function  for  random 

input . 

then  gp(jv/)  and  g(j'.;)  can  be  computed  from  the  following 
equations: 

E 
Gp(jw)= 


11 


By  cor.parins  the  tv;o  open-loop  transfer  functions,  G 

and  gCo'w),  a  hypothetical  predictor  transfer  function  P(jw) 

was  defined  as  follov;s: 


Since  this  predictor  v:as  derived  aia  thematic  ally,  its 
validity  should  be  examined  by  various  ways. 

Firstly,  hov;  reliable  is  this  predictor?  According  to  Dallos 
and  Jones,  the  predictor  should  give  a  phase  lead  starting 
fron  100  decrees  increasing  to  250  degrees  as  frequency 
increased  iron  0.5  cps  to  2.5  cps.   In  our  experiment,  the 
subject  S  was  presented  with  square  wave  stimuli  (as  shown 
in  Figure  6d).  The  frequency  distribution  of  latency  for  the 
subject  showed  that  the  existence  of  prediction  is  question- 
able. As  frequency  changed,  there  was  no  significant  shifts 
in  the  dlslrlouljion  curve.  (  The  latency  of  the  response  fall 
into  the  interval  of  100  msec  and  1pO  msec)  It  therefore 
implied  that  the  response  of  subject  S  failed  to  predict 
any  of  the  stinuli  within  the  applied  range  of  the  frequency 
of  the  square  wave. 

Secondly,  under  a  specific  frequency,  what  kind  of  distri- 
bution curve  of  latency  would  the  predictor  have?  Because 
by  examining  this  curve,  I  believe  that  the  efficiency  of 
the  predictor  could  be  obtained.  A  sharp  and  narrow  curve 
(eg.  a  nornal  distribution)  could  represent  an  effective 
predictor.   On  the  other  hand,  a  flat  and  wider  curve  (like 
rectangular  shape)  could  mean  a  weaker  one.  The  efficiency 
of  the  proposed  predictor  was  not  discussed. 

Thirdly,  since  learning  was  an  unconventional  process,  it 
should  not  be  inconceivable  that  the  predictor  ni.-ht  not  be 


12 


physically  reclined.   Hut  from  a  physiological  point  of  vie;;, 
it  would  be  an  interesting  and  meaningful  thins  to  know  the 
possible  mechanism  or  location  of  the  predictor.   But  Dallos 
and  Jones  made  no  attemp  to  suggest  it. 

(c)  Detector 

Since  the  operation  of  the  predictor  depended  upon  the 

wave  forn  of  stimulus,  there  should  be  another  element, 

namely,  detector,  which  could  exhibit  the  predictor  under 

periodic  stimuli  and  could  inhibit  it  under  aperiodic 

stimuli.  A  simple  detector  was  suggested  by  Dallos  and 

Jones.   The  detector  included  a  memory  unit  M  with  a  finite 

decay  time,  and  a  comparator  D  (Figure  12).  The  comparator 

would  continuously  compare  the  output  signal  from  the 

memory  unit  and  the  present  error  signal.   If  the  two  signals 

were  dislike,  then  the  error  signal  would  bypass  the  predictor 


^  •*>*  -I-      r^  i 


stimuli.   If  the  tv/o  signal  v;ere  alike,  then  the  error 
information  would  be  channelled  through  the  predictor. 

Based  on  this  model,  Dallos  and  Jones  tried  to  explain  the 
frequency  response  of  square  wave  stimuli.   There  were  three 
cases: 

1.  For  low  frequency  stimuli: 

Since  the  nemori  sable  information  for  a  square  wave 
appeared  to  be  the  time  duration  betv;een  the  transitions, 
therefore,  when  the  time  duration  was  longer  than  the 
memory  trace,  then  no  information  could  be  stored, 
consequently,  no  learning  process  could  proceed. 

2.  For  high  frequency  stimuli: 

Since  the  target  motion  was  too  fast,  even  with  a 
periodic  input,  the  error  signal  could  not  be  a  periodic 
one.   3o  learning  failed. 

3.  For  intermediate  frequency  G:;:.auli: 

A  steady  state  tracking  could  well  be  established.  The 


amplitude  of  distortion  in  eye  motion  was  not  significant. 
V.'ithin  this  range  of  frequency,  there  was  almost  complete 
synchronism  between  input  and  output,  therefore,  the 
memory  trace  could  not  be  continuously  reinforced.   Since 
the  memory  trace  was  assumed  to  decay  with  time,  then 
after  some  period  of  tine,  the  loss  of  synchronism  should 
be  expected.   Dallos  and  Jones  observed  that  in  the  steady 
state  tracking,  the  average  time  duration  for  good  tracking 
period  was  approximately  5  to  7  seconds.  Following  those 
good  tracking  periods,  there  were  a  few  cycles  without 
compensation. 

From  the  above  explanation  of  the  square  wave  response,  it 
seemed  to  me  that  there  were  some  points  open  for  argument: 
(a)  It  is  questionable,  that  whether  the  large  value  of 
latency  during  a  high  frequency  target  tracking  was 
cauccd  by  the  aperiodic  error  signal  or  noo.   If  we 
took  eye  muscle  into  consideration,  it  should  be  easy 
to  demonstrate  that  the  eye  could  not  move  as  fast  as 
one  wished  to.  Suppose  a  subject  was  asked  to  count 
repeatedly  "one,  two,  one,  two,  one,  ",  and  simult- 
aneously, the  subject's  eye  moved  back  and  forth 
between  two  points  in  front  of  him,  the  counting  of 
number  and  the  movement  of  the  eye  were  synchronized. 
If  the  counting  started  at  a  low  frequency,  the  eye 
could  keep  the  synchronisation  very  well.   If  the  speed 
of  counting  was  increased,  the  eye  gradually  become 
unable  to  follow.   The  back  and  forth  movement  of  the 
eye  would  get  worse  and  worse  as  the  speed  of  counting 
increased.   In  this  demonstration,  the  brain  knew  the 
speed  and  the  exact  positions  of  the  two  fixation  points, 
The  speed  c.nd  position  were  not  known  by  "learning"  but 
by  "given",   the  failure  of  the  eye  showed  that  there 


14- 


was  a  speed,  lir.itc.tior.  for  the  eye.   It  should  not  be 
confused  with  the  arbitrary  eye  movement,  namely,  the  eye 
was  asked  to  cove  bad:  and  forth  between  left  and  right 
without  specific  position  to  fixate.   In  this  case,  because 
no  accuracy  was  required,  the  eye  could  respond  faster  than 
in  the  former  case. 

In  the  case  of  eye  tracking  movement ,  the  speed  of  the 
eye  and  the  positions  for  fixation  v;ere  not  given.   If  the 
eye  could  "learn",  as  suggested  by  many  models,  it  should 
be  expected  that  the  response  would  not  be  better  than 
the  "given"  case.  Thus  the  bad  tracking  response  of  a 
high  frequency  square  wave  stimulus  could  be  caused  simply 
by  the  limitation  of  the  eye  muscle  movement.   I  was  one  of 
the  subjects.  According  to  my  own  experience,  at  high 
frequency.'  tracking,  I  could  "feel"  or  "sense"  the  frequency 
of  the  target,  over.  v.'hcr.  my  eye  failocl  to  follov.7  it. 
Therefore,  it  seemed  to  me  that  the  "learning  behavior" 
should  belong  to  the  brain,  not  to  the  eye.   Thus  when  the 
target  frequency  was  high,  and  the  eye  failed  to  track 
properly,  the  brain  still  could  "learn"  the  frequency  of 
the  target,  if  the  target  motion  was  periodic. 

(b)  There  were  many  mechanical  models  for  the  muscle.  No 

matter  which  one  was  the  best,  at  least  they  implied  that 
the  muscle  possessed  mechanical  properties.  Therefore,  it 
would  be  proper  to  assume  that  there  was  a  nature  frequency 
for  the  eye  muscle  mechanism.   If  the  frequency  of  the 
target  motion  was  close  to  the  natural  frequency  of  the 
eye  muscle  mechanism,  then  a  resonance  phenomenon  might 
happen.  This  was  probably  the  reason  for  the  good  tracking 
responses  for  the  intermediate  frequency  stimuli. 


The  above  argument  was  just  induced,  from  ''common  cense"  and 
"experimental  feclir .j" ,  no  strong  evidence  or  experimental 
results  supported  it.   However,  it  seemed  to  me  that  using 
mechanical  (or  mathematical)  model  of  physiological 
properties  to  approach  the  eye  tracking  s-stem  might  be  more 
realistic  and  practical  than  a  pure  mathematical  derivation 
or  curve  fitting. 

(2)  Sugie's  model: 

A  different  approach  to  the  stud;/  of  the  "predictive  control" 
of  the  eye  movement  v;as  carried  out  by  Sugie.  After  studying 
the  response  to  regular  square  v:ave  inputs,  he  proposed  a 
mathematical  model  of  estimation  based  on  stochastic  optimal 
control  concept  (Figure  14-  and  Figure  15).   The  variable  to 
be  estimated  was  the  period  of  the  target  notion,  and  the 
statistical  parameter  was  the  variance  of  the  estimated 
period. 

Four  assumptions  were  made,   (i)  The  estimation  depended 
upon  the  target  frequency  and  the  number  of  target  cycles, 
(ii)  The  estimated  period  of  the  target  motion  was  accom- 
panied v;ith  some  stochastic  randomness  caused  by  the 
uncertainty  of  human  memory,  (iii)  The  mean  of  the  estim- 
ated period  coincided  with  the  period  of  the  target  motion, 
because  the  probability  function  had  no  reason  to  be 
biased,   (iv)  The  variance  of  the  estimated  period  should 
depend  on  the  target  frequency  and  the  number  of  target 
cycles  (Figure  15).  A  brief  reason  for  the  last  assum- 
ption Y/as  worth  mentioning: 

(a)  The  dependence  of  the  variance  upon  target  frequency: 
As  Dallos  and  Jones  suggested,  for  a  square  wave 
input,  the  useful  information  could  be  obtained  only 
twice  a  cycle.   V/hen  frequency  was  low,  the  memory 
dec.'.y  would  cauce  uncertain  information,  therefore, 
the  variance  of  the  estimated  r>eriod  could  be  assumed 


16 


large.  However,  when  the  tnrget  frequency  was  very  high, 
the  sample  data  phenomenon  was  taking  into  account. 
Accourding  to  L.  R.  Young  and  L.  Stark-"*,  the  sampling 
period  was  250  msec.  Therefore,  when  the  input  period 
became  compatible  with  the  sampling  period,  the  change 
of  the  target  position  could  not  be  sensed  very 
accurately.  Consequently,  the  variance  of  the  estimated 
period  could  be  assumed  large.  Thus  the  variance  should 
have  its  minimum  value  at  the  intermediate  input 
frequency  range. 

(b)  The  dependence  of  the  variance  upon  the  number  of  cycles 
of  target  motion: 

As  more  information  became  available,  the  variance  of  the 
estimated  period  should  be  decreased.  Consequently,  the 
variance  of  estimated  period  should  be  a  inonotonically 
decreasing  function  of  the  number  of  cycles. 

For  simplification,  he  assumed  a  rectangular  probability 
density  function  (Figure  18),  that  is, 

/•   i 
probability  density 

2 

=  0       otherwise 

a 

The  estimation  was  assumed  to  optimise  a  "performance  index". 
This  performance  index  PI  was  defined  as  a  mean-squared  value 
of  the  length  of  time  by  which  a  stimulus  preceded  or  laged 
behind  a  response. 

(  91  O     Cy'   +   "kri-r.-*-   ~  X' 

p-r  ,  +.<-      .  fl-f-  4.  TT   Ot)o 

.r  X  =  I  w         LLUJt  ' 


2y< 


where  x  =  constant  reaction  time  without  prediction. 

t    =  ontinr.1  reaction  tine. 
opt 


The  response  of  this  r.odel  (7i~ure  1?)  rave  a  .3000.  suggestion 
for  the  possible  range  of  the  mode  an'l  average  for  the 
distribution  of  latency.  But  it  failed  to  jive  a  desired 
distribution  curve. 

As  Dallos  ar.d  Jones,  Sugie  assumed  the  memory  decayed  as  the 
only  explanation  for  the  low  frequency  square  wave  response. 
However,  he  had  a  different  explanation  for  the  higher 
frequency  response.  He  considered  the  discrete  nature  of  the 
saccadic  eye  movement  which,  I  believe,  was  more  realistic 
than  the  explanation  given  by  Dallos  and  Jonse. 

Sugie  assumed  that  the  variance  also  depended  upon  the  cycle 
number  of  the  target  notion,  that  is,  the  variance  was  a 
nonotonically  decreasing  function  of  cycle  nunber,  independent 
of  target  frequency.  Statistically,  it  should  be  true.  But 
practically,  it  would  be  doubltful.  When  conducting  experiments 
cf  a  longer  time  duration,  the  eye  night  be  fatigue,  which 
could  give  unreliable  responses.  Therefore  the  variance  could 
be  larger  as  sore  experimental  runs  were  recorded.  2n  the 
derivation  of  his  model,  Sugie  assumed  the  number  of  cycles 
of  the  target  motion  to  be  infinite.  Since  the  data  he  used 
was  fron  several  other  models,  therefore  the  cycle  numbers 
would  not  necessary  be  equal  nor  infinite.  It  seemed  to  me 
that  the  dependence  of  the  variance  upon  the  cycle  number  was 
not  a  proper  assumption. 

Another  interesting  assumption  worth  mentioning  was  concerning 
the  unbiased  probability  density  function.  A  rectangular 
function  was  assumed  for  simplification.  But  Sugie  did  not 
suggest  any  other  suitable  functions.  Whether  a  normal 
distribution  function  could  give  a  desirable  distribution 
curve  for  latency  or  not  was  worth  to  know. 


18 


(3)  Cyr  and  Fender's  model: 

After  a  number  of  predictive  models  (lender  and  ITye,  1961; 
Young  and  Stark,  1963  i  Hobinson,  1955)  for  the  eye  tracking 
system  were  proposed,  the  existence  of  the  predictive  ability 
of  the  eye  movement  was  challenged  by  Cyr  and  Fender.  Based 
on  the  study  of  human  eye  movement  in  two  dimensional 
tracking  task,  Cyr  and  Fender  found  that  the  system  was 
non-linear.  Therefore,  a  transfer  function  could,  be  derived 
for  the  oculomotor  system.  Thus  it  should  not  be  possible  to 
predict  the  response  to  one  class  of  target  motion  by  linear 

combinations  of  the  responses  to  other  classes  of  stimuli 

/\ 

(as  in  the  Dallos  and  Jon   model  )  Consequently,  the 
computation  of  a  minimum  phase  lag  (Dallos  and  Jones,  1963^; 
Young  and  Stark,  1963  )  should  not  be  possible.  Accordingly, 
the  latency  was  only  a  simple  delay  which  depended  on  the  class 
of  target  motion. 

Since  all  of  my  experimental  results  of  this  report  were  from 
one  dimensional  eye  tracking  movement,  therefore  no  comparision 
between  Cyr  and  Fender's  results  and  mine  could  be  carried  out. 
However,  there  was  a  point  which  might  be  worth  mentioning. 
In  the  one-dimensional  eye  tracking  movement,  the  ability  to 
predict  was  based  not  only  on  the  frequency  of  the  stimulus, 
but  also  on  the  shape  of  the  target  motion.  In  other  words,  the 
eye  could  predict,  if  the  stimulus  was  of  periodic  form  with 
a  intermediate  frequency.  Thus  for  disproving  the  predictive 
two-dimensional  input  with  a  intermediate  frequency  should  be 
used.  But  Cyr  and  Fender  only  used  two  kinds  of  stimuli,  one 
was  random  signal,  the  other  one  was  a  sum  of  four  small 
sinusoids  in  both  vertical  and  horizontal  directions.  Therefore, 
no  periodical  input  was  used  by  Cyr  and  Fender.  Consequently, 
their  conclusion  was  not  strong  enough. 


(B)  Sirr—o^o  ITature  Of  .77 e  Movement 

The  discrete  nature  of  the  saccadic  eye  movement  control  is 
well  established.  Since  the  introduction  of  the  sample-data 
model  by  Youn;~  and  Stark,  the  analysis  of  this  discrete 
nature  has  developed  numerous  refined  models  (see  reference 
6,  7,  8).  There  are  three  different  types  of  sample-data 
systems.  A  model  has  either  target-synchronized  or  target- 
asynchronized  properties.  A  target-synchronized  system  is 
c  ock-asynchronized.  But  a  target-asynchronized  system  can 
be  either  clock-synchronized  or  clock-asynchronized.  These 
definitions  for  the  three  types  of  sample-data  systems  are 
summarised  in  Table  2. 


desk- 


clock- 


targe t- 


STnchronlzed 


impossible 


possible 


target- 


asynchronized 


possible 


possible 


Table  2 


20 


(1  )  Latour's  experimental  results: 

In  the  early  studies  of  horizontal  eye  movement  by  Latour 

q 
and  Bouraan  ,  the  frequency  distribution  of  reaction  time 

for  both  short  run  (  Figure  24-  )  and  long;  run  (  Figure  25  ) 
were  obtained.  Latour  noticed  that,  in  short  sessions  the 
reaction  time  distribution  was  multimodal,  such  that: 

t  =  £  ±  ka 
where  t  =  reaction  time 

£  =  most  frequent  t  value 
**»  '»  2  j  3j  ~  -  —  ~ 

a  =  20  to  40  msec. 

In  longer  sessions,  this  phenomenon  faded  out*  But  the 
distribution  of  the  "difference  between  the  reaction  time 
and  its  succeeding  movements"  showed  a  similar  frequency 
distribution  curve. 

Let  *t  =  tn  -  tn+1 
where  t  =  reaction  time  at  the  nth  reaction 

t  n+-p  reaction  time  at  the  (n+1  )th  reaction 

At  =  difference  between  the  reaction  time  and 
its  succeeding  movement. 

then  the  distribution  of  *t  (  Figure  26  )  could  be  represented 


t  =  T  - 
where  ^  =  some  positive  value 

By  comparing  the  frequency  distribution  of  reaction  time  t 
and  the  frequency  distribution  of  the  At  (  Figure  26  ),  Latour 
concluded  that  there  was  a  continuous  decrease  in  the  "  most 


21 


frequent  reaction  tiae  £" ,  follov.od  by  a  relatively  fact 
increase  of  £  within  a  period  of  about  20  seconds  (  Figure 
27  ).  In  other  words,  for  a  long  session  tracking,  the  eye 
could  graduatly  shorten  its  reaction  tine  then  rapidly 
drift  back  to  the  starting  value  of  reaction  tine.  This 
cycle  could  be  continued  as  the  experiment  went  on. 

Latour's  experimental  results  and  observations  could  be  in 
the  discussion  of  the  following  .burster's  model. 

(2)  ii'orsber's  stochastic  sample-data  model: 

n 
The  studies  by  Lang'  showed  that  the  model  for  the  discrete 

nature  of  the  eye  movement  was  more  satisfactory  if  it  was 

o 

randomly  sampled.  Forster  reexanined  the  three  possible 
types  of  interosample  time  distribution  function  (  see  Table 
2,  page  19  )  with  his  revised  sample  data  model  (  Figure  19  ). 

Started  from  target — asynchronized  system,  he  assumed  that: 

L  =  t1  +  D 

where     L  =  latency 

D  =  dealy  time  from  occurrence  of  the  input  to 
the  next  occurrence  of  a  sampling  instant 
(-from  this  definition  D  should  be  strictly 
non-negative  ). 

t*  =  constant  delay  time,  as  in  Figure  20. 
fv(x)  -  probability  density  function  of  the  variable 

3C 

x  (  any  of  the  above  variables  ). 

Since  D  was  a  random  variable,  L  should  also  be  a  random 
variable,  thus  the  density  function  would  be  related  by: 


=  fy(  a 


22 


.based  on  the  assumptions  that: 

(a)  the  input  occurcd  in  as  interval  f  , 

(b)  the  time  between  inputs  were  greater  than  f   ,  the 

DloLjC 

maximum  value  of  f_ , 

C 

(c)  the  input  v/as  uniformly  distributed 
Forster  derived  out  f. 


'!) 

/fmax 


i) 


clt  ,     for  Di 


'  max  J  i) 
0  for  D*.  0 

Since  fy(-U)  was  a  non-increasing  function,  thus  it  should 
give  a  non- increasing  latency  histogram  (  Figure  21  ).  But 
the  actual  latency  distribution  increased  for  low  latencies. 
Therefore,  Forster  suggested  that  for  asynchronized  sample, 
the  eye  sometimes  was  able  to  shorten  the  sampling  intervals, 
when  a  step  v/as  observed.  This  hypothesis  could  be  supported 
if  the  function  v/as  as  follev/ed: 

0.0133  60  <T  <120 

0.0025  120  <  tr$200 

. 0  c  otherwise 

The  corresponding  simulation  latency  histogram  from  this 
function  v/as  showen  in  figure  22.  After  comparing  the 
simulations  and  the  experimental  results,  Jforster  showed 
that  the  eye  control  system  had  characteristics  of  both 
target-synchronized  and  target-asynchronized.  Lat  the  best 
sampler  logic  should  be  non-synchonized  with  a  sample  T  which 
was  composed  by  a  constant  T  plus  a  noise  n,  i.e. 

T  =  TQ  +  n  . 

examining  u'orster's  model  by  iiatour's   conclusion  and  my 
experimental  results,   two  points  should  discussed: 


(.&)  The  sar.pler  logic  of  Forstcr's  model  v;as  unifornly 

distributed  in  the  interval  of  150  to  250  mseconds.  when 
the  period  of  a  square  v:ave  stimulus  was  compatible  with 
the  sampling  interval .  then  the  change  of  target  position 
could  not  be  accurately  sensed  or  sometimes  even  missed 
(  Figure  25  ).  Thus  as  increased  percentage  of  abnormal 
responses  should  be  expected  as  the  frequency  of  the  input 
increased.  Conversely,  for  a  low  frequency  stimulus,  the 
period  of  the  input  was  much  larger  than  the  interval  of 
sampler,  thus  a  small  value  of  percentage  of  abnormal 
response  was  able  to  be  obtained.  According  to  ray 
experimental  results  shov/en  in  Figure  5  to  Figure  7»  the 
above  was  confirmed. 

(b)  In  the  assumption  of  Forster's  model,  the  latency  was 
defined  as: 

L  =  D  +  t1 

where  t.  v;as  constant  delay  time,  and  D  was  the  time  interval 
between  the  occurence  of  input  and  the  occurance  of  the 
next  sampling  instant  (  Figure  20  ).  It  should  be  obvious 
that  latency  L  was  proportional  to  the  value  of  D.  However, 
considering  Latour's  difference  phenomenon,  the  mode  of  the 
latency  distribution  curve  tend  to  decrease  as  the  time  for 
experimental  run  increased  (  Figure  27  ).  It  seemed  to  me 
that  the  decrease  of  the  mode  of  latency  should  imply  the 
decrease  of  latency.  Thus  the  value  of  D  should  also  be 
decreaseing.  The  decreasing  of  D  could  only  be  achieved  by 
shortening  the  sampling  period.  If  this  was  true,  then  the 
eye  could  sense  the  change  of  target  position  more 
accurately.  Thus,  for  a  highfrequency  stimulus,  the 
percentage  of  abnormal  response  duringa  long  session  run 
could  be  reduced,  oirice  all  of  my  experimental  runs  were 


24- 


POSSIBLE  FUTURE  SI33CTIOH 

Based  on  the  review  and  examination  of  those  models 
disscused  in  the  above  section,  some  possible  future  experi- 
ments could  be  conducted: 

(1)  For  a  furthur  understanding  of  "learning  behavior"  and 
"learning  speed",  a  detailed  comparison  of  the  difference 
between  the  response  of  continuous  stimuli  and  disconti- 
nuous stimuli  could  be  done.  Therefore,  more  experiments 
could  be  carried  out  in  this  direction. 

(2)  As  far  as  learning  behavior  as  concerned,  the  two- 
dimensional  eye  tracking  movement  should  be  tacken  into 
account.  Cyr  and  Fender  only  used  two  types  of  stimuli: 
one  was  a  random  signal,  the  other  one  was  a  sum  of  small 
sinusoids  in  both  vertical  and  horizontal  direction* 
Since  the  one  dimensional  eye  tracking  system  shov/ed  that 
the  latency  distribution  curve  v/as  both  input  freqxiency 
and  input  shape  dependent,  and  furthur  more,  it  was 
believed  that  in  some  models  a  periodic  input  with  proper 
frequency  could  be  predicted  by  the  eye,  thus  a  two- 
dimensional  periodic  input  should  be  used  in  order  to  make 
a  comparison  with  the  one  dimensional  results.  A  simple 
two-dimensional  stimulus  could  be  made  by  a  square  wave 
movement  in  both  vertical  and  horizontal  direction.  The 
response  of  this  input  might  bring  some  information  such 
as  whether  or  not  the  latency  distribution  curve  would 
shift  to  some  phase  lead  region  as  the  input  frequency 
varied  to  a  certain  range.  Ho  matter  what  kind  of  results 
could  be  obtained,  it  should  be  halpful  for  the  furthur 
analysis  of  the  "learning  behavior". 

(3)  The  oversimplification  of  Sugie's  probability  density 


function  failed  to  give  a  proper  latency  distribution 
curve.  Since  the  latency  distribution  curve  was  similar 
to  normal  distribution,  therefore,  a  probability  density 
function  similar  to  normal  distribution  might  be  reasonable 
to  try. 

(4-)  Longer  session  experimental  runs  could  be  carried  out. 
The  results  could  be  used  for  the  following  purpose: 

(a)  Re-exanine  Latour's  difference  phenomenon. 

(b)  Re-check  Dallos  and  Jones'  memory  decay  phenomenon, 
especially  the  periodic  forgetness  in  a  steady  state 
tracking  movement. 

(c)  Whether  the  percentage  of  abnormal  response  would  be 
decreased  or  not,  as  suggested  in  the  discussion  of 
this  report. 

(d)  It  might  be  useful  for  a  furthur  study  of  Forster's 
sample-data  model. 


26 


SUMMARY 

One  dimensional  eye  tracking  movement  was  measured.  Following 
types  of  stimili  were  presented,  namely,  regular  square  wave, 
irregular  square  wave  (  or  staircase  wave  ),  and  ramp  input. 
The  results  showed  that  latency  distribution  curve  was 
frequency  dependent.  For  square  wave,  the  curve  similar  to  a 
normal  distribution  shifted  back  and  forth  between  the  time 
lag  region  and  the  tine  lead  region.  For  staircase  wave,  the 
cruve  changed  its  shape  from  a  normal  distribution  to  a 
regutangular  distribution  as  frequency  increased.  The  response 
of  ramp  inputs  showed  that  when  both  continuous  and  disconti- 
nuous motion  were  involved,  the  discontinuous  portion  was 
faster  than  the  continuous  portion. 

Based  on  our  experimental  results,  the  strong  and  weak  points 
of  scnc  proposed  mcdolc  v;crc  discussed, 

(1)  Dallos  and  Jones'  model: 

(a)  Strong  point:  It  could  explain  the  response  for  square 
wave  stimili^ 

(b)  Weak  point: 

i.  The  dependence  of  learning  speed  on  the  continuity 
of  input  v/as  questionable. 

ii.  The  predictor  v/as  purely  derived  out  from  curve 
fitting  and  matheinatic  equations.  There  was  no 
simulation  results.  The  efficiency  of  the 
predictor  was  discussed.  The  existance  of  this 
predictor  was  doubtful. 

(2)  Sugie's  model: 

(a)  Strong  point: 

For  square  wave  stimuli,  the  model  could  give  a  good 
suggestion  of  the  possible  ran~e  of  the  mode  and  the 
average  of  the  latency  distribution  curve, 

(b)  Weak  point: 


27 


i.  The  dependence  of  variance  of  latency  distribu- 
tion upon  the  cycle  number  of  the  target  motion 
v/as  questionable. 
ii«  Oversimplification  of  the  probability  density 

function. 

iii.  Failed  to  predict  the  shape  of  latency 
distribution  curve. 

(3)  Cyr  and  Fender's  model: 

This  model  v;as  not  discussed  here.  It  was  only  a  reference 
to  show  a  different  point  view.  However,  it  could  be  safe 
to  say  that  the  two-dimensional  tracking  was  a  good 
approach.  But  the  type  of  stimuli  should  be  one  which  v;as 
coniprable  to  the  one-diinensional  tracking. 

(4)  Latour's  difference  phenomenon  was  reviewed  here.  This 
phenomenon  implied  G.  decreased  reaction  time  as  tho 
experimental  runs  get  longer. 

(5)  Forster's  sampl-data  was  also  reviewed.  This  target- 
asynchronized  model  could  explain  the  dependence  of  "the 
percentage  of  abnormal  response  "  upon  the  stimulus 
frequency.  But  the  experieraental  results  possessed  both 
target-synchronized  and  target-asynchronized  properties. 

Based  on  the  discussion,  some  possible  future  directions  were 
suggested.  These  directions  included  longer  session 
experimental  runs,  two-dimensional  tracking  measurements, 
comparison  between  continuous  and  discontinuous  stimuli, 
verification  of  Sugie's  model,  and  relationship  between  eye 
muscle  mechanism  and  eye  tracking  movement. 


28 


REFERENCE 

1.  D.  J.  Dallos,  and  R.  V/.  Jones,  "Learning  Behavior  of  The 
Eye  Fixation  Control  System",  IEEE  Trans,  on  Automatic 
control,  vol.  AC-3,  pp.  218-22?,  July  1563. 

2.  N.  Sugie,  "A  Model  of  Predictive  Control  in  Visual  Target 
Tracking".  IEEE  Trans,  on  System,  Men,  and  Cybernetics, 
vol.  3MC-1,  no.  1,  Jan.  1971.  pp.  2-7. 

J>.  G.  J.  3t-Cyr  and  D.  H.  Fender,  "  Nonlinearities  of  The 
Human  Oculomotor  System  Time  Delay".  Vision  Res.  vol.  9, 
pp.  14-91-1503.  Pergamon  Press  1959. 

4-.  L.  Stark,  G.  Vossius,  and  L.  R.  Young,  IEEE,  Trans,  on 
Human  Factor  in  Electronics  HFE-5,  pp.  52-57.  1962. 

5.  L.  R.  Young,  and  L.  Stark,  IEEE  Trans,  on  Human  Factors 
in  Electronics,  IIFE-4-,  pp.  32-51.  1963. 

6.  L.  Stark,  "Neurological  Control  System,  Studies  in 
Eiocngincering" .  Plenum  Press,  Nev/  York,  pp.  240-247!-, 
351-357.  1953. 

7.  G.  V.r.  Lang,  "  Representation  of  The  Human  Operator  As  A 
Sampled-  Data  System",  PhD  Thesis,  University  of  London, 

1967. 

8.  3.  M.  Forster,  2.  M.  Thesis  Report  MIT-6S-2,  Man  Veliical 
Laboratory,  Center  for  Space  Research,  HIT,  Cambridge, 
Mass.,  1968. 

9.  P.  L.  Latour,  and  M,  A.  Bouman,  "A  Non-analog  Time  Component 
in  Eye  Pursuit  Movement".  Proc.  MIT  Symposium,  1959. 

10.  P.  L.  Latour,   "The  Eye  and  Its  Tinirng" .  1961. 


29 


Muscle 


Afferent 

Si  en 


Efferent 
Signals 


Visual 
Corte:: 
17,  13,  19 


Afferent  Signals  :  continuous. 

Efferent  Signals  :  continuous  and  discret 


Fig.  1 


sampler 


target 
position 


eye 
detector 


controller 
and  plant 


eye 

position 


Fig.  2 


iris 

>  solera 

nhotocell 


subtraction 


moving  li^ht  spot 
(target) 


oscilloscope; 


.  3a. 


Fir:,  ob . 


(a) 


Signal 


Normal 
Response 


(b) 


Abnormal 
Response 


(c) 


n 


v 


L=min.  (Li>150insec.  )  ,      1=1 


Signal 


1 

1 

1 

i 

1 

1 

1 

1 

Response 


33 


0.1    or  3. 

of   occurer.ce. 


M:  .      :          ;ns. 

-.    277.15ns.      s:    75.75 


- 

5 

2 

- 

1' 

I 

200                 2                                            35;-':                 .')0 

us 


2 .    0.3   cr:  s  . 

of   occurenc • . 
51 
4- 
3 


M:    14-Oras.      Hd:    14-Or.s. 
Av:    135.56ms.      s:    33.82 


50 


100 


150 


200 


ms 


3.    0.5  ~ps « 

fr     Of     OCC. 


M:    100:as.      Md:    100ms. 
Av:    77.71ms.      s:    63.04- 


5- 

'- 

4. 

-.  ' 

1 

ML      , 

INI 

,     .     I      ,     .     .     I 

~»i5o  so      50 

0 

5 

0 

100                  150                  200      ms 

4.    0.7   cvs. 


;,'-of   occ . 


M:    -10ms.      Md:    -130.-80,-70,-30,0,30,50n3 
Av:    -7.5ms.      s:    91. 06 


3 

- 

- 

2 

' 

|     j 

50         Q 

50 

100                  200                  500               4-00          n 

ms 


5.   0.9  cps. 

2  of   occ. 


M:    -60ns.      Md:    -70,    -60ms. 
Av:    -4-9. 60ms.      s:    52.56 


c 

" 

s 

4- 

2- 

1"' 

\    I 

!       . 

1 

1CO.                 50 

0                   50                     100                       1GO 

Predictable    square  '..av/o;    Sub;    ^'j; 


1.1   c-os. 


.IS  . 

Av:    9.43ns.      s:    57.39 


ox  ucc;  . 

5 

5 

2 

1- 

j 

100 

50        0        50       100            130  ms 

7.   1.3  cps. 

II:  50ns.   Md:  -10,30ms. 

•':  Of  OCC  . 

Av:  37.04nis.   s:  48.89 

6 

• 

5- 

3- 

2 

1 

I 

i 

50 

6         50       100       150         ms 

3.  1.5  cps. 

M:  70ms.   Md:  50ins. 

V  of  occ. 

Av:  63.6833.   s:  40ms. 

8 

n 

7 

G 

5' 

4 

. 

3 

2 

1 

j 

0 

50       "100       150               ms 

9.  1.75  cps. 

M:  90ms.   Md:  100ms. 

of  occ. 

Av:  85.  00ms.   s:  53.49 

12 

11 

10 

9 

• 

8 

7 

6 

5" 

i 

I 

^> 

3' 

2 

1 

1 

1 

;  i      :  1 

| 

f                 i  

,   J_ 

35 


^-  . 

. 
s:  59.  80"         .-!-5as. 

or  occ. 

11 

10- 

9 

8- 

7 

6- 

t 

5' 

4-- 

3" 

2" 

f 

j 

X 

50 

100       150       200       250       300     ms 

\  M.  vs.  freo. 
\                   Average   x  K 

\                  Mode     Q  D 

>00 

„  \ 

^ 

Median   •  •* 

0.1   0.3   0.5  0 


Hz 


80 
70 

60 
50 


Standard  deviation 


X1          O.'j 

0.5 

0.7 

0.9     1 

1     1.3         1.5       1.  75           2 

Figure  5c 


. 


36 
( res .   ; 


:  : 

.  '    .  . 


2    - 


of  occ;. 


. 


50 


100 


150 


200 


ms 


2.      0.3  cjs.          (res. 


6 


of  occ 


I-:-.    113ns.      Md  125ras, 
Av.:    153.3;: 
i :    +55.21 


50 


0.5  cps. 

i'    Of    OCC. 

8 
6  -f 


100 


(res.  22) 


150 


200 


ms 


M:    125ms.      Md:    150ms. 
Av. :    73.8ms. 
SOJDV:    -120.79 


200   150  100   50   0   50  100   150  200   250 


ins 


14    - 

12  ' 
10  * 

8    • 
6  •' 


0.9  cps.  (res.    32) 

~  of   occ. 


II:  100ms.   Md  100ns. 
Av.:  103.67 
S'IDV:  157.45 


50   100   150   200   2=0   300   350 


ms 


(a) 


ig.    6.      Predictable    squaro  v.'uve.    Subject:    3iiiro. 


37 


1.1  Tr~. 

f  occ. 
20' 
18 


12 

1C 

8 

6 


. 

Av.:  133. 
ST. 


0 


50 


100 


150 


200 


6.   1. 


5  Hz.     (res.  51) 


M:  125ns.   I-id:  150ms 


'    o-P     ,^                                                      AV'  :     IpO.OmS. 

,r   01    occ.                                        orr»7w  .  ±zo   co 

16 

*                 -X                •       J 

14-' 

12 

10 

8- 

6 

2  ' 

C-/-1                                   xl/- 

/^/^.x^                        ^^  r—  s\ 

50 


150 


250 


7.   1.5  Hz.     (res.  65) 
#  cf  occ. 


M:  150ns.   lid:  150ms. 
Av.:  136.11ns. 


±MJV  :    —   pu.  /  i 

22 

20 
18 

16 
14 

12 
10' 

8 
6 
4-' 

2 

""  1  ;  [•  

50                  100                  150                  200 

ins 


iS.  6b. 


1.7 


(resp. 


M:  12>-.i.  .     :     as, 

Av.  :  1  .  .   ••".c; . 


,,••   <j^.   wwv--  * 

STW:  -   .  ! 

14 

12 

10 

8 
6' 

4-' 

2  ' 

| 

!     I           i 

50 

100     150     200    250            350   ms 

9.   1.9  Hz.    (resp.  46,  abnormal  33)     M:  162.5ns.   Kd:  150ns, 


1C1 

8 

of  occ. 

^  i  v  •  •     i  s  *—  '  »'*•-'  x^^    * 

STDV:  I  65.23 

6' 

''  I 
2' 

1 

1C 

50     100     150     200     250               ms 

10.   2.3  Hz.    (resp.  29,  abnormal  4-8) 


M:  125ms.  I-ld:  150~3, 
Av.:  113.96ms. 


10 

#  of  occ. 

**  V   •   »         >   .1  Nu/  •   ^/  'w/i-H  I™/  * 

STDV:  I  73.39 

8 

- 

6 

2 

i  I 

.   ! 

-50    6    56    100 

150    200     250     300ns 

11.   2.5  Hz.    (resp.  52,  abnormal  80) 
$  of  occ. 


M:  100ms.   Md:  100ms. 
Av.:  126.08ms. 
STDV:  I  77.30 


10 

8 

6' 

) 

4-  ' 

2" 

; 

i      ,  t 

50 

100 

150     200    250      300         m: 

Fi-%  6c. 


39 


175 

150 
125 
100 


Average  X- 
I-Iode  Q- 
i'ledian  *• 


D.I      0.3  0.5          0.9     1.1   1.3  1-5  1.7  1.9         2.3  2.5          Hz 


Standard  deviation 


0.1  0.3  0.5     0.9  1.1  1.3  1.5  1.7  1.9     2.3  2.5 


Hz 


Vir;.  3d. 


1.   .   :is.   (resp.  5) 


2.  0.5  Hz.    (resp.  16) 


of  occ. 

or  occ. 

5 

4' 

4 

3 

3  • 

2 

2 

I    ! 

1 

1 

i 

1        i 

100     200   as 

(   •   ,      I 

100     200       ras 

M:  200ns.   Md:  2?0ms.          M:  100mc.   Md:  100ms. 

;-.v:  132.5ns.  s:  68.46         Av:  105.5zas.  s:  46.8 

c 

3.  0.5  Hz.    (resp.  22)          4.  0.?  Hz.    (resp.  25) 

of  occ. 

-/?  of  occ  . 

7- 

6" 

6- 

5' 

5- 

4 

4- 

3 

3- 

0+                          2- 

I 

in    i    |  i   1 

•  I 

—  f—  i  —  '  •    —      i    r- 

1                        I 

-50   0  50  100    ns 

-150   -50  o   50  100   i 

M:  50ms.   Md:  100ns.           M:  -25ms.   Md:  -50ms. 

Av:  51.2ms.  s:  76.9           AV:  -2ns.    s:  74.9 

5.  0.?  Hz.    (resp.  30) 

;  of  occ.                    M:  -25nis.   Md:  Oas. 

10- 

Av:  -22ns.    s:  59-r-is. 

9- 

Q 

0 

7 

6" 

5 

• 

4- 

3: 

2- 

1 

1; 

100  ;:o   o  50  100    ns 

(a) 


?iS.  7:  Prodictable  sour.ro  v;ave.  Subjsct;:  S. 


6.  1.1  Hz.    (resp.  34) 


M:  Ons.   Md:  Cms. 


10 

of  occ. 

s  :    GO          .-.v  : 

9 

8- 

7 

6 

5- 

4- 

3 

2- 

1 

-100  -50     ( 

)     50     100            200            300              ms 

7.  1.3  Hz.    (resp.  50) 


20 

18- 

16 


12 
10 

8 

6-  • 

4 

2 


of  occ  . 


-50   o  50  100 


200 


M:  Oms.   Md:  Oms. 
s:  48.5  Av:  18ras, 


300 


ms 


8.  1 

10- 

9 


5  Hz.    (resp.  46) 
of  occ. 


M:  25ms.   Md:  25ms. 
s:  68.8   Av:  14.6:23, 


•c 

7 

6' 

5 

."• 

5 

! 

- 

1 

* 

i         i 

} 

I    .    !    . 

s\  r-  r\ 

c 

r\       r\          c.r\    ir\r\                onr\                znn             m 

42 


•"I     r'  "          —             (  -p.  - 

ir 

':3.         're 

sp  .   4-6 

of   occ. 

~f     .~>"C 

-  ^  # 

25 

, 

_  _  9 

24 

^•s 

22- 

21 

20 

19 

• 

18 

17 

16 

15 

14 

13 

- 

12 

11 

• 

10 

9 

- 

8 

7 

6- 

5 

- 

3 

4 

2- 

1 

1 

"  ,  i 

1       ,  '  I  , 

0       50    100  1= 

~C 
?0         ms 

0               1 

DO            200       300     as 

M:    75ms.      i:i: 

100ms. 

H:    100ms.      ] 

•Id:    100ms. 

200 
150- 

msec. 

T-Tr>^« 

^i  ^>/-\ 

\x_ 

IMUU.I 
p^  r*  ~  '  ci  r\  ' 

100 

>    ^ 

D—     -0,1'iea. 

/r^  x^AVe] 

cm 

50 

^•^/^""^ 

x///\^-X 

N-^,^r^i^'3ta3 

CS.QQ           X             X 

idard 

\.7 

QQ          ,>r"^---:3 

0.1   0.3  3-5  \v 

^Kl.1   1.3  1. 

5     1.75     2 

Hz. 

-50- 

or 

Pig.   7c. 


-;.  j.1J,   0.257,  0.468  Hz.' 


resp.:  f  .       •  '     .   -'id: 
abnor::'il:  2. 


\J 

J.    VJO 

**  • 

V:  -   ','.^3 

20 

18 

16  • 

12 

10 

8 

6 

t 

4 

2  ' 

• 
I 

50 

150 

250     350     450     550     650   ms 

2.  0.235,  0.488,  0.785  Hz.    resp.:  90.    M:  150ms.   Kd:  150ms. 
Av.:  167.70ns. 
#  of  OGC-                             STDV:  -  52.48. 

30' 

28  ' 

26  ^ 

24 

.-.2  -  - 

20- 

18' 

16- 

14- 

12- 

10- 

8- 

6- 

4- 

2 

- 

\ 

50 

1CO 

150     200    250     300     350  ms 

Fiq,  8:  Unpredictable  3P\;r.rc  wave.   Subject:  G. 


44 


• 

.    ,   .   >,   ,23  Hz. 
of  occ. 

.  :               '        . 

:    .    Av.  :  179.  1m  • 
DV:  -   .   . 

20 

16 

14 

•12  ' 

10 

8' 

6 

4' 

2  • 

'             100    150     200     250     300     ms 

4.  0.73?,  1.23,  1.43  Hz. 

#  of  occ. 

24i 
22 

20' 

15- 


14 
12 

10" 
8-- 

6' 

4" 

2 


resp.: 


K:  175ns.  Kd:  150ns 
Av.:  199.32ms. 
STDV:  I  73.4. 
c 


100  .  150   200   250   300  350   400   450   500   ns 


5.  1.23,  1<48,  1.71  Hz. 
#  of  occ. 


resp.:  45. 
abnormal :  7 . 


I-I:  200ms.  I-Id: 
Av.:  2Q7.95ms. 
STDV:  -  66.2. 


14- 

12- 

10- 

8- 

r.  • 

4- 

2 

i 

! 

1        . 

•0 

150    200     250     500     550     400 

**•? 


6.      1.43,    1.71, 


r- 

«     •  • 

•          •'I  l\ 

t 


M:  .         L:    125ms. 


STDV:    -133.5. 

4 

2 

I 

i 
,     I 

ns 

1C  -                                                                 5CO            £OC            700 

7.       1.71,  1.95,  2.21       . 
,7  of  occ. 

4i 


res:..:     21.  M:    15Cms.      KG:    ICO, 

abnormal:    10^.  125, 

150ms. 
Av.:   159.52ms. 

STDV:    -   65.98 


50 


1  150  2:  250  300 


ns 


8.        1.95,    2.21,    2.45  Hz.  resp.:    26. 


M:    125ns. 


_y     ^j>     «#•  n                                                                                                        '  fOt            •"•V  .  :       IO°«  >--'-"a  • 

//-      '-'-i-        ^  -^    -^«                                                                                                                                                                                                    T~  o<~7      ^>^v 

oxijv  :    -o/.Oi 

4- 

3- 

2. 
1- 

L 

1 

56           100        15           200      250        5C 

0       350                       as 

9. 


P 

,      <£- 


res?.:    19.  M:   175ms. 


7- 

#  of  occ. 

ctijxiui;  JCLX;     ^o^>«          ^i.v.:           o.^  ;..:.. 

SJDV:   1  48.'     . 

6' 

5- 

>^  - 
2- 

1- 

i 

r 

__                  «1^Oi                     -->  ,-.,->                     OC^O                      Xr^~' 

'    '.    oC. 


4-3 


10.       2.4-5,   2.73,    5.0" 


3  r 

2 
1  4- 


occ, 


recr>. :    1 " . 

: 


150 


250 


M: 
.  : 
:     - 


300       ms 


200 
150 

100 


msec 


i 


Average     X- 

;-:ed-  *- 

Ilodel         a- 


}' 

\.  .../: 

\  ** 

-v    V 

,     \ 

Standard 

.    o.evi-.oion 

123^4 

567 

-i        of— 

10              order 
exrjer. 

1:  0.15,    0.235,    0.-':-33,  Us. 

2;  :0.235,    0.4SG,  0.735,  Hz. 

3:  0.4-88,   0.785,  1.230,  Hz. 

4-:  0.735,    1.230,  1.4-80,  Hz. 

5:  1.230,    1.4-30,  1.710,  Hz. 

6:  1.4-SC,    1.?10,  1.950,  Hz. 

7:  1.710,    1.9?0,  2.210,  Hz. 

3:  1.950,    2.210,  2.4-^0,  Hz. 

9:  2.210,   2.450,  2.750,  Hz. 

10:  2.4-50,    2.730,  3.010,  Hz. 


Pis.   8d. 


4-7 


.   •   .   , 

ccc. 

28 

26 

24 
22 

20 
18 
16 
14 
12 
10" 

8 
6 
4 

2 


:  10. 


-100 


(UN      -I  ro-v,-. 
• 

.  :  . 

•     -          .7 


50   100   150   200   250   500   $50  400 


ms 


2.      0.235,    0.433,    0.755  Hz. 
if-  of  occ. 


2? 
261 

24 

22 

20 

16 

12 

8 

6- 


resp.:    67.  M:    150ras.      Md:    1,50ns. 

abnormal:    3.         Av.:   161.15ns. 

SO?L>Y:    -   54.67. 


50  100  150  200  250  300  350  400 


ms . 


Unpredictable  ccuare  ucve.   out;'    :     ^o. 


17  -i  rr 
-  J.    ,. 


ab.  :  :        . 


26 
24 
22 
20 

16 

14 

12- 

10 

8 

6 
^ 

o 


f     OCC. 


100  1.  D 


.  «  • 

A.V.  :  .3. 

STBV:    - 


ms 


0.755,   1.23' 

rr    OT     uCC. 


r~  s~\          s\  r~  ••% 

— ^j    o      50 


Hz. 


resp. :  77. 
abnormal:  32. 


150     250 


450 


M:    200ms.      Md:    200ns 
Av.:    2Q2ias. 


20 
18 

16 
14 

c 

12 

10 

8 

6 

4- 

2; 

I               ,     i     ,     ,     ,     '          , 

ns 


5.  i.::33,  1.430,  1.7"<0  Hz. 

;•'•  ol  occ. 
10 


resp.:    52. 


M:    225ns.      Md:    2503S. 
Av.:    211.G7r.s. 
STDV:    i   53.99 


4 

2 

i  ! 

i 

100             2-JO             500 

400 

500 

600 

ns 

49 


.  1.710, 


Hz 


res  .  :   i. 

abnor:"-!:   1 


100 


300 


M:  2,   ;.   lid:  ?.r-Cns. 
Av.  : 


u.u     uu^; 

3TLV:    -       ' 

14 

12 

10 

i 

8 

6 

4- 

2 

.     !      I 

i 

ins 


7.   1.710,  1.950,  2.210  Hz. 

#  of  occ. 
10 


res-.:  41.      M:  250ms.   Md:  250ms, 
abnormal:  209.  Av.:  220.38ns. 

SOJDV:  i  128.58. 


8 

6 

2 

)     I 

I 

1       I                           ! 

50 


150 


250    350 


4-50 


550 


ins, 


8.  1.950,  2.210,  2.450  Hz. 


#  Ox  OCC, 


resp.:  13. 
abnormal:  58. 


M:  225ms.   Md:  200, 

250ns . 

Av.:  234.62ns. 
STDV:  -  66.57. 


4 

2 

i 

I     I 

I 

i 

=  100 


200 


300 


400 


ms 


9.   2.210,  2.450,  2.730  Hz. 
#  of  occ. 


resp.:  23.      M:  200ms.   Md:  150ns 


6  ' 
2  ' 

1             i 

'     !         ! 

STBV:    --124 

.   !   !         LJ          ,             •      » 

' 

.M.vs.  freq. 


300 


500 


ins 


Average  x  —  x 

"Median  •  -  • 

'.ode    a  -  G 


deviation 


50 


1. 


• 

24 

* 
/N        •               • 

TL  '    0-217 
'   ccc. 

-       .                        .  :          .                                           .             : 
-2".                          1:     '    .             ".  :    1^    .  "1ns. 
:     -     7.6v. 

22 

- 

20 

13 

- 

16 

12  • 

10 
8- 

6 

2- 

;    i 

i     !     ,     , 

50 


100 


150 


200 


250 


300 


ns 


2.        /\  :    0.3--6  PIz.        i  3°. 
XL:    0.217  Hz.        -  3°. 

#  of  occ. 


8 

6 


resp.:36. 


M:    150ms.      Md:    150ms. 
S^DV:    -  69.06! 


-175 


-100 


0 


100 


200 


300     ms 


3.   A  :  0.r-55  Hz. 
:  0.3S'i-  Hz. 


16 
14 
12" 
10 

6' 
4. 

21 


of  occ. 


resp.:  43.      H:  150ns.   I'd:  150ns. 
•abnormal:  30.   Av.:  156.97mc. 

STDV:  -  32.42. 


30 


100 


Fig.  10.:  Unpredictable  sif-nv.-.l.   Subj-co:  './ang. 


:        - 

J\  :  0  . 


. :    23 . 


-   .     -  _  . 

Av .  :     ' 

'.  :    -          .        , 


\ 
14 

12 

10 

8- 
6 


occ. 


5',}     100     15D     2  ::'.:•   '-'      '       '     350     4CT     4-^0     $00 


ns 


5 .       A  :   0 . 3 

n :  0.217 

#  of   occ. 

8-- 

6 
4 
p 


rasp.:    32. 
?rr.al:    4. 


M:    150ns.      Hd:    150ms, 
Av. :  ,06ms. 

STDV:    I  62. -3. 


100 


150 


260  250 


300 


350        ns 


6.       A   :    0-5?G  Hz. 
:    0.217  :-:z. 


+     - 


.:    60.  M:    150ras.      Md:    l5Cas, 

abnoriaals    11.        Av.:    "\y\.    2an. 

3TDV:    *70.7*. 


y  o 

I  OCC  . 

12' 

10' 

B- 

& 

2' 

i 

I 

i  i  ;  i    __] 

100       200       300       400       500     ms 

Fi-r.      Ob. 


52 


200 

150 

100  - 
50 


msec 


tandard  deviation 


order  of 
experiments. 


Pig.  10c. 


55 


?v;o  1:3  '        .ular  -;ave: 


a* 
b. 


•?,:•;-:    edr;ej 
Dro    '         edge: 


1 


7-*  o  <?  —  A  **^  c*  r\  • 

-lo-'  •      *  1 .    • 


r.odir-.r.:    M    . 


nedian:    M,. 


1.        2  /S9C.    ?"po   a. 
Tots.1  rospcnsa: 


:     Of      OCC. 


' 


h 

• 

2  • 

.Ml 

•-^0          100           -15Q            200            2^0            LIS 

- 

isir.rj  edro:           M.,:    200ms 

DroDir.r  ed^e:        •;,:    1->Cc.s. 
c. 

r.  « 

/r 

6- 

/.  - 

t 

4 
i  i-  i 

I 

2- 

.    nif 

50     100            200              n 

s                              .     50      100   1  JO  200  250     rr 

ri;3.    11:    P.o.-p  fimc-'cior..      Subject;:    '/anj; 


54- 


o  OC/~"~  -1 ^     v  '.'      .      •",  ' '  '••  •  <~  '         •      ?f^-r-  .      17,fy,~ 

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d' 


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1  ,                   .    _          -    I 

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7.    0.33  /sec.    C"pe  a.   Ht:  2; Ons.   II:  225ns, 


of  occ. 


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350        ms 


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100 


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--J- -»-»—.*—«-  (l-~l  I  >  i  ». 

100     150    200     250 


ms 


Pic;.  11c. 


56 


600  -• 
550 

500 

450 
400 
350  -- 

300  -' 
250  - 

200  •- 

150 


msec. 


07T53     0.5    0133 
0.33     0.7     1 


Total  response: 

-1-!  CT-  T-  -.  -T^-^  . 

Drop  in:;  edge: 


1.6 


/sec 


Fir.  11 d. 


57 


Sinusoid: 
Latencies  (i 


20C 


10( 


0.5   1.0   1.5   2.0 


freq. 


Square  wave 
Latencies (ms) 


50Q 


200 


100 


100 


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-- o— 


-« — e- 


or..v.  st 
c;-clo  1 
cycle  2 
cycle  3 


Fir;.  12 


c(t) 


r(t)  =  target  motion 
c(t)  =  eye  motion 
1-1=  memory  unit 
D=  comparator 
P(ov;)=  predictor 
g(jw)=  plant 


FiS.13 


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